One side of the rectangle is 6 cm larger than the other side. If the larger side is reduced by 2 times

| January 8, 2021 | education

One side of the rectangle is 6 cm larger than the other side. If the larger side is reduced by 2 times, and the smaller one is increased by 2 cm, then the perimeter of the new rectangle will decrease by 6 cm. Find the sides of this rectangle.

1. Take as x (cm) the length of the smaller side of the rectangle, the length of the larger side
(x + 6) cm.
2. The perimeter of the original rectangle is 2x + 2 (x + 6) = (4x + 12) cm.
3. The length of the larger side after its decrease by 2 times will become equal to (x + 6) / 2 cm, the length of the smaller side after its increase by 2 cm will become equal to (x + 2) cm.
4. The perimeter of the resulting rectangle is 2 (x + 6) / 2 + 2 (x + 2) = (3x + 10) cm.
5. We make the equation:
(4x + 12) – (3x + 10) = 6;
x = 4 cm – the length of the smaller side.
4 + 6 = 10 cm – the length of the larger side
Answer: the length of the larger side of the original rectangle is 10 cm, the length of the smaller side is 4 cm.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.